| Summary: | This thesis concerns the theoretical pricing and hedging of options, financial instruments
that give a payoff at a set date based on the price of one, or several other financial assets,
known as the underlying assets. The underlying assets are usually taken to be stocks, but
can also be bonds, securities, portfolios, or other financial instruments. In this thesis we
study two types of options - life contingent options and barrier Asian options. Because the
options examined in this thesis are relatively uncommon, with a novel mechanism of action,
they are known as exotic options. The analysis takes place in a stylised mathematical
model of a financial market known as the Black-Scholes model. We show for the life
contingent option that there exists a minimal super-hedging portfolio and determine the
associated initial investment. We also give a characterisation of when replication of the
option is possible. Next, we investigate the pricing problem for barrier Asian options with
short maturity times. Due to the nature of Asian options, closed form formulae for the fair
price of the option are relatively difficult to obtain. Using novel results from the theory
of stochastic calculus, we obtain closed form asymptotic formulae for the price of short
maturity barrier Asian options. Finally, we demonstrate our results with some explicit
examples.
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